Tiffany, Ivory, Wendy and Kathy jointly contributed to the cost of a present for their colleague. Tiffany's contribution is ¹₂ of the total contribution made by the four girls. The ratio of Kathy's contribution to the total of Ivory's and Wendy's contribution is 5 : 2. What is the total contribution by the four girls if Ivory's contribution is ¹₃ of Wendy's contribution and the total amount contributed by Tiffany and Kathy is $240?

Tiffany	Ivory	Wendy	Kathy	Total
1x14	1x14			2x14
	2x2		5x2
	1x1	3x1
14 u	1 u	3 u	10 u	28 u

Working backwards.

Total amount that Ivory and Wendy had is the combined repeated identity.
LCM of 2 and 4 = 4

Total amount that Ivory, Wendy and Kathy had is the next combined repeated identity.
LCM of 1 and 14 = 14 

Total amount contributed by Tiffany and Kathy
= 14 u + 10 u
= 24 u

24 u = 240

2 u = 240 ÷ 24 = $10

Total contribution by the four girls
= 28 u
= 28 x 10
= $280

Answer(s): $280